New Hampshire State Standards for Mathematics: Grade 12
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NH.M:N&O:12. NECAP - High School - Grade Level Expectation: Number and Operations.
M:N&O:12:1. Demonstrates conceptual understanding of rational numbers by knowing why a real number is rational if and only if the number's decimal expansion eventually repeats or terminates.
M:N&O:12:2. Demonstrates understanding of the relative magnitude of real numbers by solving problems that involve ordering or comparing any subset of the real numbers.
M:N&O:12:3. No standard listed at this level.
M:N&O:12:4. Accurately solves problems involving scientific notation or uses significant digits to assess the precision of an answer. Interprets rational exponents and their relation to radicals; computes by hand in simple cases, and using a calculator when appropriate. Interprets numbers given in scientific notation and carries out computations of them with and without a calculator. Solves problems involving compound interest.
M:N&O:12:5. No standard listed at this level.
M:N&O:12:6. No standard listed at this level.
M:N&O:12:7. Makes appropriate estimates in a given situation by determining the level of accuracy needed and analyzing the accuracy of results.
M:N&O:12:8. Applies properties to determine whether a given subset of numbers is closed under a given arithmetic operation.
NH.M:G&M:12. NECAP - High School - Grade Level Expectation: Geometry and Measurement.
M:G&M:12:1. No standard listed at this level.
M:G&M:12:2. Creates formal proofs of propositions (e.g. angles, lines, circles, distance, midpoint and polygons including triangle congruence and similarity).
M:G&M:12:3. No standard listed at this level.
M:G&M:12:4. Applies the concepts of congruency by using matrices to represent reflections, translations, and rotations.
M:G&M:12:5. Applies the concepts of similarity of right triangles with the trigonometric functions defined as ratios of sides of triangles, and uses the ratios of the sides of special right triangles (30-60-90 and 45-45-90) to determine the sine, cosine and tangent ( 30,45, 60) and solve related problems.
M:G&M:12:6. Solves problems involving angles, lengths and areas of polygons by applying the trigonometric formulas (law of sines/cosines, ) ; and applies the appropriate unit of measure.
M:G&M:12:7. Uses informal concepts of successive approximation, upper and lower bounds, and limits in measurement situations (e.g., use successive approximation to find the area of a pond); uses measurement conversion strategies (e.g., unit/dimensional analysis).
M:G&M:12:8. No standard listed at this level.
M:G&M:12:9. Solves problems involving circles as loci of points in the plane satisfying certain distance requirements, and uses the distance formula to obtain equations for circles.
M:G&M:12:10. Demonstrates conceptual understanding of spatial reasoning and visualization by performing and justifying constructions with compass and straightedge or dynamic geometric software.
NH.M:F&A:12. NECAP - High School - Grade Level Expectation: Functions and Algebra.
M:F&A:12:1. Identifies arithmetic and geometric sequences and finds the nth term; then uses the generalization to find a specific term.
M:F&A:12:2. Demonstrates conceptual understanding of linear and nonlinear functions and relations by representing and analyzing functions in several ways; recognizing properties of functions and characteristics properties of families of functions; applying knowledge of functions to interpret, model, and solve problems; analyzing characteristics of classes of functions (polynomial, rational, and exponential) to include domain, range, intercepts, increasing and decreasing intervals and rates of change; representing functions numerically, algebraically, graphically, and verbally (i.e. in written words), recognizing properties of a function from these representations, and transfers information from one representation to another; graphing polynomial, rational and exponential functions, including vertical and horizontal shifts, stretches, and compressions as well as reflections across vertical and horizontal axes; applying knowledge of functions to interpret and understand situations, design mathematical models, and solve problems in mathematics as well as in natural and social sciences. (Local)
M:F&A:12:3. Demonstrates conceptual understanding of algebraic expressions by manipulating, evaluating, and simplifying algebraic and numerical expressions; adding, subtracting, multiplying and dividing polynomials; adding, subtracting, multiplying and dividing rational expressions; simplifying complex fractions; factoring quadratic and higher degree polynomials, including difference of squares; applying properties of logarithms and converting between logarithmic and exponential forms; manipulating, evaluating, and simplifying expressions involving rational exponents and radicals and converting between expressions with rational exponents and expressions with radicals.
M:F&A:12:4. Demonstrates conceptual understanding of equality by solving equations and systems of equations or inequalities and interpreting the solutions algebraically and graphically; by factoring, completing the square, using the quadratic formula, and graphing quadratic functions to solve quadratic equations; solving and interpreting solutions of equations involving polynomial, rational, and radical expressions; analyzing the effect of simplifying radical or rational expressions on the solution set of equations involving such expressions; finding approximate solutions to equations by graphing each side as a function using technology. (Understand that any equation in x can be interpreted as the equation f(x) = g(x) and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).); solving 2x2 and 3x3 systems of linear equations and graphically interprets the solutions; solving systems of linear and quadratic inequalities; solving and graphically interpreting solutions systems of equations involving nonlinear expressions. (Local)
NH.M:DSP:12. NECAP - High School - Grade Level Expectation: Data, Statistics, and Probability.
M:DSP:12:1. Interprets a given representation(s) (e.g., regression function including linear, quadratic, and exponential) to analyze the data to make inferences and to formulate, justify, and critique conclusions.
M:DSP:12:2. Analyzes patterns, trends, or distributions in data in a variety of contexts by calculating and analyzing measures of dispersion (standard deviation, variance, and percentiles).
M:DSP:12:3. Organizes and displays one- and two-variable data using a variety of representations (e.g., box-and-whisker plots, scatter plots, bar graphs, line graphs, circle graphs, histograms, frequency charts, linear, quadratic, and exponential regression functions) to analyze the data to formulate or justify conclusions, make predictions, or to solve problems with or without using technology.
M:DSP:12:4. Uses counting techniques to solve problems in context involving combination or permutations using a variety of strategies (e.g., nCr, nPr, or n!); and finds unions, intersections, and complements of sets.
M:DSP:12:5. For a probability event in which the sample space may or may not contain equally likely outcomes, predicts the theoretical probability of an event and tests the prediction through experiments and simulations; compares and contrasts theoretical and experimental probabilities; finds the odds of an event and understands the relationship between probability and odds.
M:DSP:12:6. In response to a teacher or student generated question or hypothesis decides the most effective method (e.g., survey, observation, research, experimentation) and sampling techniques (e.g., random sample, stratified random sample) to collect the data necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the questions or hypotheses being tested while considering the limitations of the data that could effect interpretations; and when appropriate makes predications, asks new questions, or makes connections to real-world situations.
NH.M:N&O:AM. Advanced Mathematics - Grade Level Expectation: Number and Operations.
M:N&O:AM:1. Demonstrates conceptual understanding of the real number system as an extension of the rational numbers by representing real numbers as infinite decimal expansions (that provide successive rational approximations to the number) and as points on a number line. Determines whether the decimal expansion of a rational number given in fractional form eventually repeats or terminates (without using a calculator).
M:N&O:AM:2. No standard listed at this level.
M:N&O:AM:3. No standard listed at this level.
M:N&O:AM:4. Accurately solves problems and demonstrates understanding of complex numbers by interpreting them geometrically and by computing with them ( e, g., adding, multiplying, dividing, finding the nth root, or by finding conjugates). Understands complex numbers as an extension of the real numbers (e.g. arising in solutions of polynomial equations). Manipulates complex numbers using rectangular and polar coordinates. Knows the fundamental theorem of algebra and knows that non-constant polynomials always factor into linear factors over the complex numbers.
M:N&O:AM:5. No standard listed at this level.
M:N&O:AM:6. No standard listed at this level.
M:N&O:AM:7. No standard at this level
M:N&O:AM:8. Applies properties to add and multiply numerical matrices with attention to the arithmetic properties of these operations. Algebraically and geometrically interpret vectors, vector addition, and scalar multiplication in the plane, with attention to arithmetic properties. Knows and uses the principle of mathematical induction.
NH.M:G&M:AM. Advanced Mathematics - Grade Level Expectation: Geometry and Measurement.
M:G&M:AM:1. No standard listed at this level.
M:G&M:AM:2. Extends and deepens knowledge and usage of proofs and proof techniques; and uses geometric models to represent and distinguish between Euclidean and non-Euclidean Systems.
M:G&M:AM:3. No standard listed at this level.
M:G&M:AM:4. No standard listed at this level.
M:G&M:AM:5. No standard listed at this level.
M:G&M:AM:6. Solves problems involving volume using Cavalieri's principle and derives and uses formulas for lengths of arcs and areas of sectors and segments of circles.
M:G&M:AM:7. Uses radian measure appropriately when solving problems; converts between radian measure and degree measure; and understands why radian measure is useful.
M:G&M: AM:8. No standard listed at this level.
M:G&M:AM:9. Solves problems using analytic geometry (including three-dimensions) and circular trigonometry (e.g., find the equation of a circle inscribed in a triangle; find the distance between opposite vertices in a rectangular solid); explores and interprets the characteristics of conic sections graphically and algebraically including understanding how different planar slices of a double cone yield different conic sections; knows the characterization of conic sections as loci of points in the plane satisfying certain distance requirements, and uses the distance formula to obtain equations for the conic sections.
M:G&M:AM:10. No standard listed at this level.
NH.M:F&A:AM. Advanced Mathematics - Grade Level Expectation: Functions and Algebra.
M:F&A:AM:1. Identifies and computes partial sums of infinite arithmetic and geometric sequences, determines when an infinite geometric series converges, and finds its sum. Connects arithmetic and geometric sequences to linear and exponential functions, respectively.
M:F&A:AM:2. Demonstrates conceptual understanding of linear and nonlinear functions and relations from a set-theoretic perspective, and operations on functions including composition and inverse including computing inverses algebraically; analyzing characteristics of classes of functions and inverse functions (exponential, logarithmic, trigonometric) to include domain, range, intercepts, increasing and decreasing intervals and rates of change, periodicity, end behavior, maximum and minimum values, continuity, and asymptotes; analyzing properties of functions including injectivity (1-1), surjectivity (onto), critical points and inflection points. Determine graphically and analytically whether a function is even, odd or neither; analyzing informally the idea of continuity and limits; recognizing properties of families of functions including logarithmic and trigonometric, and graphs them; analyzing domain restriction and the effects of it on the function and its properties.
M:F&A:AM:3. Demonstrates conceptual understanding of algebraic expressions by using the remainder theorem, the factor theorem and rational root theorem for polynomials; by factoring polynomials over integer, rational, real and complex numbers.
M:F&A:AM:4. Demonstrates conceptual understanding of equality by solving equations and verifying identities involving trigonometric expressions; solving, graphing and interpreting equations involving exponential and logarithmic expressions; interpreting systems as matrix equations and solving them by computing the appropriate matrix inverse and multiplication, with or without technology; applying the intermediate value theorem to find exact or approximate solutions of equations or zeros of continuous functions.
NH.M:DSP:AM. Advanced Mathematics - Grade Level Expectation: Data, Statistics, and Probability.
M:DSP:AM:1. No standard listed at this level.
M:DSP:AM:2. Analyzes and interprets measures of dispersion (standard deviation, variance, and percentiles) and central tendency for the normal distribution; and interprets the correlation coefficient and the coefficient of determination in the context of data.
M:DSP:AM:3. Uses technology to explore the method of least squares and median-median for linear regression.
M:DSP:AM:4. No standard listed at this level.
M:DSP:AM:5. Solves probability problems (e.g., by applying concepts of counting, random variables, independence/dependence of events, and conditional probability).
M:DSP:AM:6. No standard listed at this level.